Sometimes inferences made at some specific time are valid at other times, too. In model-based diagnosis and monitoring as well as qualitative simulation inferences are often re-done although they have been performed previously. We propose a new methodforsharingpredictions done at different times, thus mutually cutting down prediction costs incurring at different times. Furthermore, we generalize the technique from `sharing predictions across time' to sharing predictions across time and logical contexts'. Assumptionbased truth maintenance is a form of sharing predictions across logical contexts. Because of the close connections to the ATMS we were able to use it as a means for implementation. We report empirical results on monitoring different configurations of ballast water tanks as used on offshore platforms and ships.